09/12/2022

Qatar World Cup 2022: from the World Cup logo to VAR

Team lineups, mascot selection, facts about Qatar, and the rules of the sport. During the World Cup, any topic about what happens on and off the field is relevant. Among the many curiosities in the world of sports, we've selected some facts about the 2022 Qatar World Cup especially for fans of mathematics and football.

The principle used in visualizing Richarlison's goal is being studied at IMPA.

The goal by Richarlison, the Brazilian national team striker, made headlines around the world, including in the American newspaper, the NY Times . On an interactive 3D page, the newspaper showcases three impressive goals from the 2022 Qatar World Cup, also including plays by Argentinian Lionel Messi and American Christian Mate Pulisic.

The tool reproduced the players' positions during the play, with visualization created by artificial intelligence. The program works using implicit neural networks, that is, computational models inspired by the functioning of the human brain. The technique is being studied by Visgraf (Computer Graphics Laboratory of IMPA) to represent a surface.

“In the case of the visualization of Richarlison's goal, each frame is representing a different surface with the neural network. They make the movement, but it's not very realistic because the application of the animation is still in progress. In our case, we are working on the representation of a single surface, which we have already managed to do very well,” stated postdoctoral researcher Tiago Novello.

The group published a paper on the topic during the SIBGRAPI 2022 (Conference on Graphics, Patterns and Images) event on visual computing. Check out more information at this link.

Video Assistant Referees (VAR) is inspired by mathematical work.

The Video Assistant Referees (VAR) is a video system that assists the on-field referee in identifying potential errors during a match. For each play requiring intervention, a team of referees and assistant referees analyze the erroneous or doubtful plays using VAR technology.

The precursor to this technique is the Virtual Referee, created by a group of researchers from Visgraf and TecGraf (PUC-Rio). In a three-dimensional environment, images of the field were taken with indications of the official dimensions of the grass and the positions of the ball and players. This makes it possible to position the cameras at key points for observing the play. It is necessary to have more than one camera to compare angles, since the physical world has three dimensions, while camera images only have two dimensions.

Widely used on TV channels to show the match in detail and popularly known as the old "tie-breaker," the Virtual Referee was conceived by researchers Paulo Cezar Pinto Carvalho (Visgraf/IMPA), Flávio Szenberg (TeCGraf/PUC-Rio), and Marcelo Gattass (TeCGraf/PUC-Rio).

Luiz Velho, lead researcher at Visgraf, spoke about the topic on the program Hiperconectado, presented by Atila Iamarino on TV Cultura. The program is available on YouTube.

“To relate real objects in the physical world to mathematical models, you need to use coordinates. There are sensors that capture the position of points in space. The camera takes information from the 3D world and projects it onto the image, which is in 2D. If you have a ball on the field, it is in a certain position in the three-dimensional world and another when captured by the camera, in the two-dimensional world. With projective geometry, we can relate these coordinates and calculate the exact position of that ball,” Luiz stated.

The VAR system used in Qatar is an evolution of the previous technology, with faster and more sophisticated equipment. Called "Semi-automated offside technology ," the new technology uses 12 tracking cameras under the stadium's roof to track the ball and the exact position of each player on the field.

Estádio da Copa Catar 2022 durante o jogo Uruguai x Coreia do Sul – Foto de Heo Manjin – Ministry of Culture, Sports and Tourism Official / Wikimedia Commons

Symbol of the Qatar 2022 World Cup

Another interesting fact about the World Cup is its official logo , which, in addition to symbolizing the World Cup trophy, alludes to the number eight – the number of stadiums in the tournament.

According to its creators, the 3D design reveals a perfect circle when rotated, symbolizing planet Earth and a soccer ball. The emblem also references the infinity symbol, which is often associated with the Möbius strip – the IMPA logo!